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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="classes2.html#NM1">Universe</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="zf_refle.html#NM1">Subclass</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="zf_lang.html#NM2">ZF-formula</a>;<br/>







<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="zf_lang.html#NM2">ZF-formula</a>] means  <a href="zf_fund1.html#K7" target="_self">Diagram</a> <font color="Maroon">a<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>assume </b><a NAME="E1:47"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> is <a href="zf_fund1.html#V8" target="_self">closed_wrt_A1-A7</a> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E2:47"/><b>then </b><i><font color="Green">E51</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M2">Element</a> of  <a href="zf_lang.html#K1">VAR</a>  holds <br/>( <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font> <a href="zf_lang.html#K4">'='</a> <font color="Olive">b<sub>2</sub></font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font> <a href="zf_lang.html#K5">'in'</a> <font color="Olive">b<sub>2</sub></font>] )
 
<b>by </b><i><a class="ref" href="zf_fund1.html#T18" target="_self">Th18</a></i>;<br/>
<a NAME="E3:47"/><i><font color="Green">E52</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="zf_lang.html#NM2">ZF-formula</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[ <a href="zf_lang.html#K6">'not'</a> <font color="Olive">b<sub>1</sub></font>]
 
<b>by </b><i><a class="txt" href="zf_fund1.html#E1:47"><i><font color="Green">E50</font></i></a>, <a class="ref" href="zf_fund1.html#T19" target="_self">Th19</a></i>;<br/>
<a NAME="E4:47"/><i><font color="Green">E53</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="zf_lang.html#NM2">ZF-formula</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>2</sub></font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font> <a href="zf_lang.html#K7">'&amp;'</a> <font color="Olive">b<sub>2</sub></font>]
 
<b>by </b><i><a class="txt" href="zf_fund1.html#E1:47"><i><font color="Green">E50</font></i></a>, <a class="ref" href="zf_fund1.html#T20" target="_self">Th20</a></i>;<br/>
<a NAME="E5:47"/><i><font color="Green">E54</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="zf_lang.html#NM2">ZF-formula</a><br/>for <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M2">Element</a> of  <a href="zf_lang.html#K1">VAR</a>  st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[ <a href="zf_lang.html#K8">All</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font>]
 
<b>by </b><i><a class="txt" href="zf_fund1.html#E1:47"><i><font color="Green">E50</font></i></a>, <a class="ref" href="zf_fund1.html#T21" target="_self">Th21</a></i>;<br/>
<a NAME="E6:47"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="zf_lang.html#NM2">ZF-formula</a> holds <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 
<b>from </b><i><a class="ref" href="zf_lang1.html#S1">ZF_LANG1:sch 1</a>(<a class="txt" href="zf_fund1.html#E2:47"><i><font color="Green">E51</font></i></a>, <a class="txt" href="zf_fund1.html#E3:47"><i><font color="Green">E52</font></i></a>, <a class="txt" href="zf_fund1.html#E4:47"><i><font color="Green">E53</font></i></a>, <a class="txt" href="zf_fund1.html#E5:47"><i><font color="Green">E54</font></i></a>);<br/></i>
<b>hence </b><a NAME="E7:47"/>
 <a href="zf_fund1.html#K7" target="_self">Diagram</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>


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